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The structural compliance of annular ring gear can significantly influence the quasi-static and dynamic performance of an epicyclic gear set. As powertrain components are continually being optimized to their design limits, this influence becomes prominent and can no longer be ignored. The current paper will study the impact of ring gear compliance on the dynamic response of epicyclic gear sets in fixed ring kinematic configuration. To achieve this objective, the current study will incorporate a finite element-based ring gear formulation into the three-dimensional planetary load distribution model of Ryali and Talbot (2021, "A Dynamic Load Distribution Model of Planetary Gear Sets," Mech. Mach. Theory, 158, p. 104229). The proposed model employs a modified simplex algorithm to iteratively solve for the elastic gear mesh contacts in conjunction with a numerical integration scheme, which enables it to inherently capture the influence of several components and system-level design variations. The developed formulation is used to conduct parametric studies involving different planetary gear designs, ring gear fixtures (bolted vs. splined), and operating conditions (quasi-static, dynamic). In the case of a splined ring gear fixture, an external splined tooth contact model is developed, which will be used to validate the model against the quasi-static experiments of Kahraman et al. (2010, "Influence of Ring Gear Rim Thickness on Planetary Gear Set Behavior," ASME J. Mech. Des., 132(2), pp. 0210021-0210028). The discussed results demonstrate the fidelity of the developed model, thus making it an excellent tool for the design and analysis of planetary gears with thin annular ring gears. [ABSTRACT FROM AUTHOR]

This study presents a unique experimental methodology that synchronously measures various quasi-static responses of a simple four-planet planetary gear set, namely, planet load sharing, overall transmission error (OTE), and floating sun gear orbits. Strain gauges mounted directly on the planet pins were used to monitor the load shared among the planets, which is a crucial design criterion for durability and performance. High-precision optical encoders were used to measure the OTE of the gear set to explore its diagnostic value in identifying system errors. Radial motions of the floating sun gear, which are critical to the self-centering and load sharing behavior of the gear set, were monitored using magnetic proximity probes. The influence of various design parameters and operating conditions such as planet mesh phasing, carrier pin position errors, gear tooth modifications, and input torque on the system's response will be investigated by performing an extensive set of experiments in a repeatable and accurate manner. Finally, these experimental results will be recreated theoretically using the static planetary load distribution model of Hu et al. (2018, "A Load Distribution Model for Planetary Gear Sets," ASME J. Mech. Des., 140(5), p. 53302) to not only validate the model but also comprehend the measured behavior. [ABSTRACT FROM AUTHOR]